Flux-limited Diffusion Approximation Research Articles

Radiation transport methods in star formation simulations

Radiation transport plays a crucial role in star formation models, as certain questions within this field cannot be accurately addressed without taking it into account. Given the high complexity of the interstellar medium from which stars form, numerical simulations are frequently employed to model the star formation process. This study reviews recent methods for incorporating radiation transport into star formation simulations, discussing them in terms of the used algorithms, treatment of radiation frequency dependence, the interaction of radiation with the gas, and the parallelization of methods for deployment on supercomputers. Broadly, the algorithms fall into two categories: i) moment-based methods, encompassing the flux-limited diffusion approximation, M1 closure, and variable Eddington tensor methods, and ii) methods directly solving the radiation transport equation, including forward and reverse ray tracing, characteristics-based methods, and Monte Carlo techniques. Beyond discussing advantages and disadvantages of these methods, the review also lists recent radiation hydrodynamic codes implemented the described methods.

The birth and early evolution of a low-mass protostar

Context. Understanding the collapse of dense molecular cloud cores to stellar densities and the subsequent evolution of the protostar is of importance to model the feedback effects such an object has on its surrounding environment, as well as describing the conditions with which it enters the stellar evolutionary track. This process is fundamentally multi-scale, both in density and in spatial extent, and requires the inclusion of complex physical processes such as self-gravity, turbulence, radiative transfer, and magnetic fields. As such, it necessitates the use of robust numerical simulations. Aims. We aim to model the birth and early evolution of a low-mass protostar. We also seek to describe the interior structure of the protostar and the radiative behavior of its accretion shock front. Methods. We carried out a high resolution numerical simulation of the collapse of a gravitationally unstable 1 M⊙ dense molecular cloud core to stellar densities using 3D radiation hydrodynamics under the gray flux-limited diffusion approximation. We followed the initial isothermal phase, the first adiabatic contraction, the second gravitational collapse triggered by the dissociation of H2 molecules, and ≈247 days of the subsequent main accretion phase. Results. We find that the subcritical radiative behavior of the protostar’s shock front causes it to swell as it accretes matter. We also find that the protostar is turbulent from the moment of its inception despite its radiative stability. This turbulence causes significant entropy mixing inside the protostar, which regulates the swelling. Furthermore, we find that the protostar is not fully ionized at birth, but the relative amount of ionized material within it increases as it accretes matter from its surroundings. Finally, we report in the appendix the results of the first 3D calculations involving a frequency-dependent treatment of radiative transfer, which has not produced any major differences with its gray counterpart.

Large-Scale Convection during Gravitational Collapse with Neutrino Transport in 2D and 3D Models on Fine Grids

The problem of the gravitational collapse of the core of a massive star is considered, taking into account the neutrino transport in the flux-limited diffusion approximation. To reduce the computational domain of a multidimensional problem on a fixed computational grid, the core of a star, which is already at the stage of collapse, is considered. Since the collapse stage is delayed in time compared to the gas-dynamic time scale for an emerging proto-neutron star, we consider the mathematical problem for the initial configuration in equilibrium and neglected the initial radial velocity. Pressure for a long time at the collapse stage is provided by relativistic degenerate electrons, so the relationship between pressure and density in the initial configuration is described by a polytropic equation with the polytropic index n=3. The purpose of this paper is to test the hypothesis that large-scale convection is independent of the 2D and 3D geometry of the mathematical problem and computational grid parameters, as well as the choice of the initial stage of gravitational collapse. The scale of convection is determined by the size of the region of decreasing entropy with neutrino losses, i.e., nonequilibrium neutronization, and the presence of a weak initial rotation.

Compatible and energy conserving multi-material arbitrary Lagrangian Eulerian scheme for multi-group radiation hydrodynamics simulations

A compatible, bounds preserving and energy conserving multi-material arbitrary Lagrangian Eulerian (ALE) scheme suitable for an unstructured mesh is developed for multi-group radiation hydrodynamics (RHD) simulation of various high energy density physics (HEDP) phenomena involving large material deformations, such as intense thermal radiation or high-power laser driven systems. In order to study very short time scale HEDP phenomena, the electron and ion energy equations (with the effect of electron-ion energy relaxation) are solved separately with an assumption of single macroscopic fluid velocity for each species (two-temperature hydrodynamics model). The governing multi-material hydrodynamics equations are solved by using a higher-order cell-centered hydrodynamics (CCH) scheme. In multi-material flows, the remapping step introduces mixed computational cells in which multiple materials exist in a single cell. Therefore, material interfaces in mixed cells are required to be reconstructed and tracked. In our implementation, this is achieved by using moment-of-fluid (MOF) method. The information of these interfaces is further used to formulate an interface aware sub-scale dynamics (IASSD) scheme for multi-material closure in mixed computational cells. The IASSD scheme is generalized for the two-temperature hydrodynamics model in which separate equations are used to update the electron and ion energies. The multi-group radiation transport on an unstructured mesh is computed using a cell-centered, monotonic, nonlinear finite volume (NLFV) scheme. The flux-limited diffusion (FLD) approximation is used to recover the free-streaming limit of the radiation propagation in optically thin regions. In the ALE step, the electron, ion and radiation energies due to MG-RHD model are conservatively remapped using a center-of-mass (CM) reconstruction of the fields and a compatible and energy conserving remapping scheme. An exact integration based on the intersection between the new (rezoned) and old meshes is used in the remap step. Similar procedure is followed for the remap of cell mass and cell-centered momentum components. In this paper, the details of a compatible, bounds preserving and conservative ALE scheme developed for MG-RHD are described. The remapping of relevant physical quantities due to multi-physics models implemented in the code such as non-local electron energy transport are also discussed. Several validation test problems including laser driven shock propagation in multi-material geometries are provided to demonstrate the accuracy and performance of the ALE scheme implemented.

A Multidimensional Multicomponent Gas Dynamic with the Neutrino Transfer in Gravitational Collapse

The self-consistent problem of gravitational collapse is solved using 2D gas dynamics with taking into account the neutrino transfer in the flux-limited diffusion approximation. Neutrino are described by spectral energy density, and weak interaction includes a simplified physical model of neutrino interactions with nucleons. I investigate convection on the stage of the collapse and then in the center of the core, where the unstable entropy profile was probably formed. It is shown that convection has large scale. Convection appears only in the semitransparent region near the neutrinosphere due to non-equilibrium nonreversible neutronization. Convection increases the energy of emitted neutrino up to 15÷18 MeV. The obtained neutrino spectrum is important for the registration of low-energy neutrinos from a supernova.

Flux-limited Diffusion Approximation Models of Giant Planet Formation by Disk Instability. II. Quadrupled Spatial Resolution

Abstract While collisional accumulation is nearly universally accepted as the formation mechanism of rock and ice worlds, the situation regarding gas giant planet formation is more nuanced. Gas accretion by solid cores formed by collisional accumulation is the generally favored mechanism, but observations increasingly suggest that gas disk gravitational instability might explain the formation of at least the massive or wide-orbit gas giant exoplanets. This paper continues a series aimed at refining three-dimensional (3D) hydrodynamical models of disk instabilities, where the handling of the gas thermodynamics is a crucial factor. Boss (2017, 2021) used the β cooling approximation to calculate 3D models of disks with initial masses of 0.091 M ⊙ extending from 4 to 20 au around 1 M ⊙ protostars. Here we employ 3D flux-limited diffusion (FLD) approximation models of the same disks, in order to provide a superior treatment of disk gas thermodynamics. The new models have quadrupled spatial resolution compared to previous 3D FLD models, in both the radial and azimuthal spherical coordinates, resulting in the highest spatial resolution 3D FLD models to date. The new models continue to support the hypothesis that such disks can form self-gravitating, dense clumps capable of contracting to form gas giant protoplanets, and suggest that the FLD models yield similar numbers of clumps as β cooling models with β ∼ 1 to ∼10, including the critical value of β = 3 for fragmentation proposed by Gammie.

New boundary conditions for the approximate flux-limited diffusion radiative transfer in circumstellar environments

Context. In order to constrain the models describing circumstellar environments, it is necessary to solve the radiative transfer equation in the presence of absorption and scattering, coupled with the equation for radiative equilibrium. However, solving this problem requires much CPU time, which makes the use of automatic minimisation procedures to characterise these environments challenging. Aims. In this context, the use of approximate methods is of primary interest. One promising candidate method is the flux-limited diffusion (FLD), which recasts the radiative transfer problem into a non-linear diffusion equation. One important aspect for the accuracy of the method lies in the implementation of appropriate boundary conditions (BCs). We present new BCs for the FLD approximation in circumstellar environments that we apply here to spherically symmetric envelopes. Methods. At the inner boundary, the entering flux (coming from the star and from the envelope itself) may be written in the FLD formalism and provides us with an adequate BC. At the free outer boundary, we used the FLD formalism to constrain the ratio of the mean radiation intensity over the emerging flux. In both cases we derived non-linear mixed BCs relating the surface values of the mean specific intensity and its gradient. We implemented these conditions and compared the results with previous benchmarks and the results of a Monte Carlo radiative transfer code. A comparison with results derived from BCs that were previously proposed in other contexts is presented as well. Results. For all the tested cases, the average relative difference with the benchmark results is below 2% for the temperature profile and below 6% for the corresponding spectral energy distribution or the emerging flux. We point out that the FLD method together with the new outer BC also allows us to derive an approximation for the emerging flux. This feature avoids additional formal solutions for the radiative transfer equation in a set of rays (ray-tracing computations). Conclusions. The FLD approximation together with the proposed new BCs performs well and captures the main physical properties of the radiative equilibrium in spherical circumstellar envelopes.

Protoplanetary Disk Birth in Massive Star-forming Clumps: The Essential Role of the Magnetic Field

Abstract Protoplanetary disks form through angular momentum conservation in collapsing dense cores. In this work, we perform the first simulations with a maximal resolution down to the astronomical unit (au) of protoplanetary disk formation, through the collapse of 1000 M ⊙ clumps, treating self-consistently both non-ideal magnetohydrodynamics with ambipolar diffusion as well as radiative transfer in the flux-limited diffusion approximation including stellar feedback. Using the adaptive mesh-refinement code RAMSES, we investigate the influence of the magnetic field on the disks properties with three models. We show that, without magnetic fields, a population dominated by large disks is formed that is not consistent with Class 0 disk properties as estimated from observations. The inclusion of magnetic field leads, through magnetic braking, to a very different evolution. When it is included, small <50 au disks represent about half the population. In addition, about 70% of the stars have no disk in this case, which suggests that our resolution is still insufficient to preserve the smaller disks. With ambipolar diffusion, the proportion of small disks is also prominent and we report a flat mass distribution around 0.01–0.1M ⊙ and a typical disk-to-star mass ratios of ∼10−2–10−1. This work shows that the magnetic field and its evolution plays a prominent role in setting the initial properties of disk populations.

Impact of dust diffusion on the rim shape of protoplanetary disks

Context. Multiple mechanisms are known to give rise to turbulence in protoplanetary disks, which facilitates the accretion onto the central star. Small dust particles that are well coupled to the gas undergo diffusion due to this turbulent motion. Aims. This paper investigates the influence of turbulence-induced dust diffusion on the equilibrium of protoplanetary disks. Methods. The model accounts for dust sublimation, radiative transfer with the flux-limited diffusion approximation, and dust diffusion. It predicts the density and temperature profiles as well as the dust-to-gas ratio of the disk. Results. It is shown that dust diffusion can have a large impact: Assuming the dust survives for 104 s or longer before it can be evaporated, this leads the dust diffusion to widen the inner disk considerably. This effect is generated through a feedback mechanism as the diffusion length is much shorter than the disk width. With increasing dust diffusion, the inclination of the inner rim toward the stellar radiation becomes steeper until it is almost vertical. The temperature range of evaporation and condensation, which is linked to the dust composition, has no influence on this effect. Conclusions. For realistic parameters, dust diffusion cannot be neglected when determining the equilibrium of the disk. Stronger turbulence inside the disk induces more dust diffusion. Therefore, the dust density grows more gradually over a greater distance and less radiation reaches the disk surface. The new equilibrium shape of the disk is more inclined toward the star. This effect is universal and independent of the specific dust composition.

Birth of convective low-mass to high-mass second Larson cores

Context. Stars form as an end product of the gravitational collapse of cold, dense gas in magnetized molecular clouds. This fundamentally multi-scale scenario occurs via the formation of two quasi-hydrostatic Larson cores and involves complex physical processes, which require a robust, self-consistent numerical treatment. Aims. The primary aim of this study is to understand the formation and evolution of the second hydrostatic Larson core and the dependence of its properties on the initial cloud core mass. Methods. We used the PLUTO code to perform high-resolution, one- and two-dimensional radiation hydrodynamic (RHD) core collapse simulations. We include self-gravity and use a grey flux-limited diffusion approximation for the radiative transfer. Additionally, we use for the gas equation of state density- and temperature-dependent thermodynamic quantities (heat capacity, mean molecular weight, etc.) to account for effects such as dissociation of molecular hydrogen, ionisation of atomic hydrogen and helium, and molecular vibrations and rotations. Properties of the second core are investigated using one-dimensional studies spanning a wide range of initial cloud core masses from 0.5 M⊙ to 100 M⊙. Furthermore, we expand to two-dimensional (2D) collapse simulations for a selected few cases of 1 M⊙, 5 M⊙, 10 M⊙, and 20 M⊙. We follow the evolution of the second core for ≥100 years after its formation, for each of these non-rotating cases. Results. Our results indicate a dependence of several second core properties on the initial cloud core mass. Molecular cloud cores with a higher initial mass collapse faster to form bigger and more massive second cores. The high-mass second cores can accrete at a much faster rate of ≈10−2 M⊙ yr−1 compared to the low-mass second cores, which have accretion rates as low as 10−5 M⊙ yr−1. For the first time, owing to a resolution that has not been achieved before, our 2D non-rotating collapse studies indicate that convection is generated in the outer layers of the second core, which is formed due to the gravitational collapse of a 1 M⊙ cloud core. Additionally, we find large-scale oscillations of the second accretion shock front triggered by the standing accretion shock instability, which has not been seen before in early evolutionary stages of stars. We predict that the physics within the second core would not be significantly influenced by the effects of magnetic fields or an initial cloud rotation. Conclusions. In our 2D RHD simulations, we find convection being driven from the accretion shock towards the interior of the second Larson core. This supports an interesting possibility that dynamo-driven magnetic fields may be generated during the very early phases of low-mass star formation.

Direct collapse to SMBH seeds in cosmological halos with radiation transfer

AbstractWe present results of our zoom-in cosmological hydrodynamic simulations of direct collapse (DC) to supermassive black hole (SMBH) seeds with radiative transfer (RT). The DC has been modeled in dark matter halos of ∼108M⊙, using adaptive mesh refinement (AMR) code Enzo. For the first time, the baryonic collapse has been followed down to 10−7 pc (∼0.01 AU) with on-the-fly RT and the flux-limited diffusion (FLD) approximation. We find a complex behavior involving accretion flow and associated outflows driven by the radiation force. The resulting gas dynamics around the central density peak differs profoundly from that in previous works which adopted adiabatic approximation in the core. The core forms with a photosphere at ∼1 AU, and its growth starts to saturate at ∼100M⊙. The unrelaxed core radiates intermittently near the Eddington luminosity, correlated with strong anisotropic outflows.

Non-LTE radiation hydrodynamics in PLUTO

Context. Modeling the dynamics of most astrophysical structures requires an adequate description of the interaction of radiation and matter. Several numerical (magneto-) hydrodynamics codes were upgraded with a radiation module to fulfill this request. However, those that used either the flux-limited diffusion (FLD) or the M1 radiation moment approaches are restricted to local thermodynamic equilibrium (LTE). This assumption may not be valid in some astrophysical cases. Aims. We present an upgraded version of the LTE radiation-hydrodynamics (RHD) module implemented in the PLUTO code, which we have extended to handle non-LTE regimes. Methods. Starting from the general frequency-integrated comoving-frame equations of RHD, we have justified all the assumptions that were made to obtain the non-LTE equations that are implemented in the module under the FLD approximation. An operator-split method with two substeps was employed: the hydrodynamics part was solved with an explicit method by the solvers that are currently available in PLUTO, and the non-LTE radiation diffusion and energy exchange part was solved with an implicit method. The module was implemented in the PLUTO environment. It uses databases of radiative quantities that can be provided independently by the user: the radiative power loss, and the Planck and Rosseland mean opacities. In our case, these quantities were determined from a collisional-radiative steady-state model, and they are tabulated as functions of temperature and density. Results. Our implementation has been validated through different tests, in particular, radiative shock tests. The agreement with the semi-analytical solutions (when available) is good, with a maximum error of 7%. Moreover, we have proved that a non-LTE approach is of paramount importance to properly model accretion shock structures. Conclusion. Our radiation FLD module represents a step toward a general non-LTE RHD modeling.

NADA-FLD: a general relativistic, multidimensional neutrino-hydrodynamics code employing flux-limited diffusion

ABSTRACT We present the new code NADA-FLD to solve multidimensional neutrino-hydrodynamics in full general relativity (GR) in spherical polar coordinates. The energy-dependent neutrino transport assumes the flux-limited diffusion approximation and evolves the neutrino energy densities measured in the frame comoving with the fluid. Operator splitting is used to avoid multidimensional coupling of grid cells in implicit integration steps involving matrix inversions. Terms describing lateral diffusion and advection are integrated explicitly using the Allen–Cheng or the Runge–Kutta–Legendre method, which remain stable even in the optically thin regime. We discuss several toy-model problems in one and two dimensions to test the basic functionality and individual components of the transport scheme. We also perform fully dynamic core-collapse supernova (CCSN) simulations in spherical symmetry. For a Newtonian model, we find good agreement with the M1 code ALCAR, and for a GR model, we reproduce the main effects of GR in CCSNe already found by previous works.

The Impact of Accretion Heating and Thermal Conduction on the Dead Zone of Protoplanetary Disks

Abstract The paper investigates the influence of accretion heating and turbulent heat conduction on the equilibrium of protoplanetary disks, extending the 2D axisymmetric passive disk model of Flock. The model includes dust sublimation and radiative transfer with the flux-limited diffusion approximation, and predicts the density and temperature profiles as well as the dust-to-gas ratio of the disk. It is shown that the accretion heating can have a large impact: for accretion rates above 5 · 10−8 M ⊙ yr−1 a zone forms behind the silicate condensation front with sufficiently high temperature to sublimate the dust and form a gaseous cavity. Assuming a Prandtl number ∼0.7, it is furthermore shown that the turbulent heat conduction cannot be neglected in the evaluation of the temperature profile. While the inner rim position is not affected by viscous heating, the dead zone edge shifts radially outward for higher accretion rates.

Supernova Explosion Mechanism with the Neutrinos and the Collapse of the Rotation Core

Most of the energy released in the gravitational collapse of the cores of massive stars is carried away by neutrinos. Neutrinos play a pivotal role in explaining core-collapse supernovae. In this work the multidimensional gas dynamics is used with neutrino transport in the flux-limited diffusion approximation to study the role of multi-dimensional effects. The possibility of large-scale convection is discussed, which is interesting both for explaining SNII and for setting up observations to register possible high-energy (≲10 MeV) neutrinos from the supernova. In compare with the previous work describing a new multidimensional gas dynamics method with neutrino transport we investigate the role of the rotation in the convection.

Dynamics of multiple protoplanets embedded in gas and pebble discs and its dependence on Σ and ν parameters

Protoplanets of super-Earth size may get trapped in convergence zones for planetary migration and form gas giants there. These growing planets undergo accretion heating, which triggers a hot-trail effect that can reverse migration directions, increase planetary eccentricities, and prevent resonant captures of migrating planets. In this work, we study populations of embryos that are accreting pebbles under different conditions, by changing the surface density, viscosity, pebble flux, mass, and the number of protoplanets. For modelling, we used the FARGO-THORIN two-dimensional (2D) hydrocode, which incorporates a pebble disc as a second pressure-less fluid, the coupling between the gas and pebbles, and the flux-limited diffusion approximation for radiative transfer. We find that massive embryos embedded in a disc with high surface density (Σ = 990 g cm−2 at 5.2 au) undergo numerous “unsuccessful” two-body encounters that do not lead to a merger. Only when a third protoplanet arrives in the convergence zone do three-body encounters lead to mergers. For a low-viscosity disc (ν = 5 × 1013 cm2 s−1), a massive co-orbital is a possible outcome, for which a pebble isolation develops and the co-orbital is further stabilised. For more massive protoplanets (5 M⊕), the convergence radius is located further out, in the ice-giant zone. After a series of encounters, there is an evolution driven by a dynamical torque of a tadpole region, which is systematically repeated several times until the co-orbital configuration is disrupted and planets merge. This may be a way to solve the problem that co-orbitals often form in simulations but they are not observed in nature. In contrast, the joint evolution of 120 low-mass protoplanets (0.1 M⊕) reveals completely different dynamics. The evolution is no longer smooth, but rather a random walk. This is because the spiral arms, developed in the gas disc due to Lindblad resonances, overlap with each other and affect not only a single protoplanet but several in the surrounding area. Our hydrodynamical simulations may have important implications for N-body simulations of planetary migration that use simplified torque prescriptions and are thus unable to capture protoplanet dynamics in its full glory.

Direct collapse to supermassive black hole seeds with radiation transfer: cosmological haloes

We have modeled direct collapse of a primordial gas within dark matter halos in the presence of radiative transfer, in high-resolution zoom-in simulations in a cosmological framework, down to the formation of the photosphere and the central object. Radiative transfer has been implemented in the flux-limited diffusion (FLD) approximation. Adiabatic models were run for comparison. We find that (a) the FLD flow forms an irregular central structure and does not exhibit fragmentation, contrary to adiabatic flow which forms a thick disk, driving a pair of spiral shocks, subject to Kelvin-Helmholtz shear instability forming fragments; (b) the growing central core in the FLD flow quickly reaches ~10 Mo and a highly variable luminosity of 10^{38}-10^{39} erg/s, comparable to the Eddington luminosity. It experiences massive recurrent outflows driven by radiation force and thermal pressure gradients, which mix with the accretion flow and transfer the angular momentum outwards; and (c) the interplay between these processes and a massive accretion, results in photosphere at ~10 AU. We conclude that in the FLD model (1) the central object exhibits dynamically insignificant rotation and slower than adiabatic temperature rise with density; (2) does not experience fragmentation leading to star formation, thus promoting the fast track formation of a supermassive black hole (SMBH) seed; (3) inclusion of radiation force leads to outflows, resulting in the mass accumulation within the central 10^{-3} pc, which is ~100 times larger than characteristic scale of star formation. The inclusion of radiative transfer reveals complex early stages of formation and growth of the central structure in the direct collapse scenario of SMBH seed formation.

Large-scale Instability during Gravitational Collapse with Neutrino Transport and a Core-Collapse Supernova

Most of the energy released in the gravitational collapse of the cores of massive stars is carried away by neutrinos. Neutrinos play a pivotal role in explaining core-collape supernovae. Currently, mathematical models of the gravitational collapse are based on multi-dimensional gas dynamics and thermonuclear reactions, while neutrino transport is considered in a simplified way. Multidimensional gas dynamics is used with neutrino transport in the flux-limited diffusion approximation to study the role of multi-dimensional effects. The possibility of large-scale convection is discussed, which is interesting both for explaining SN II and for setting up observations to register possible high-energy (≳10MeV) neutrinos from the supernova. A new multi-dimensional, multi-temperature gas dynamics method with neutrino transport is presented.

Shaken and stirred: the effects of turbulence and rotation on disc and outflow formation during the collapse of magnetized molecular cloud cores

We present the results of eighteen magnetohydrodynamical calculations of the collapse of a molecular cloud core to form a protostar. Some calculations include radiative transfer in the flux-limited diffusion approximation while others employ a barotropic equation of state. We cover a wide parameter space, with mass-to-flux ratios ranging from $\mu = 5$ to $20$; initial turbulent amplitudes ranging from a laminar calculation (i.e. where the Mach number, $\mathscr{M} = 0$) to transonic $\mathscr{M} = 1$; and initial rotation rates from $\beta_\mathrm{rot} = 0.005$ to $0.02$. We first show that using a radiative transfer scheme produces warmer pseudo-discs than the barotropic equation of state, making them more stable. We then `shake' the core by increasing the initial turbulent velocity field, and find that at all three mass-to-flux ratios transonic cores are weakly bound and do not produce pseudo-discs; $\mathscr{M} = 0.3$ cores produce very disrupted discs; and $\mathscr{M} = 0.1$ cores produce discs broadly comparable to a laminar core. In our previous paper (arXiv:1701.08741), we showed that a pseudo-disc coupled with sufficient magnetic field is necessary to form a bipolar outflow. Here we show that only weakly turbulent cores exhibit collimated jets. We finally take the $\mathscr{M} = 1.0$, $\mu = 5$ core and `stir' it by increasing the initial angular momentum, finding that once the degree of rotational energy exceeds the turbulent energy in the core the disc returns, with a corresponding (though slower), outflow. These conclusions place constraints on the initial mixtures of rotation and turbulence in molecular cloud cores which are conducive to the formation of bipolar outflows early in the star formation process.

Direct Collapse to Supermassive Black Hole Seeds with Radiative Transfer: Isolated Halos

Direct collapse within dark matter (DM) halos is a promising path to form supermassive black hole (SMBH) seeds at high redshifts. The outer part of this collapse remains optically thin, and has been studied intensively using numerical simulations. However, the innermost region of the collapse is expected to become optically thick and requires us to follow the radiation field in order to understand its subsequent evolution. So far, the adiabatic approximation has been used exclusively for this purpose. We apply radiative transfer in the flux-limited diffusion (FLD) approximation to solve the evolution of coupled gas and radiation, for isolated halos. For direct collapse within isolated DM halos, we find that (1) the photosphere forms at ~10^{-6} pc and rapidly expands outward. (2) A central core forms, with a mass of ~1 Mo, supported by thermal gas pressure gradients and rotation. (3) Growing thermal gas and radiation pressure gradients dissolve it. (4) This process is associated with a strong anisotropic outflow, and another core forms nearby and grows rapidly. (5) Typical radiation luminosity emerging from the photosphere encompassing these cores is ~5 x 10^{37}-5 x 10^{38} erg/s, of order the Eddington luminosity. (6) Two variability timescales are associated with this process: a long one, which is related to the accretion flow within the central ~10^{-4}-10^{-3} pc, and ~0.1 yr, which is related to radiation diffusion. (7) Adiabatic models have been run for comparison and their evolution differs profoundly from that of the FLD models, by forming a central geometrically-thick disk. Overall, an adiabatic equation of state is not a good approximation to the advanced stage of direct collapse, mainly because the radiation in the FLD is capable of escaping due to anisotropy in the optical depth and associated gradients.